A "clock spring" mechanism as has been used in cars for many years to connect the steering wheel devices to the rest of the car. Of course, that does not allow continuous rotation in one direction, but as there are no moving contacts, it is probably electronically fairly quiet.
Googling that produces connectors that can bend, I need one that can spin on it's axis.
This is for a school project to make a rotating inverted pendulum using an arduino that can (hopefully) be programmed through the hub. I figure that robot club would benefit from learning PID with an inverted pendulum.
A 4 pole jack ought to be ok for this, you wont be programming while the thing is trying to balance.
A couple of machines were I work have industrial multi slip ring units to take power, air & data to rotating parts of the machine, power goes through slip rings, but cat5 goes via an optical connection, thinking about it its a reliable connection unaffected by contact resistance & dust etc.